Free Access
Issue
Math. Model. Nat. Phenom.
Volume 5, Number 4, 2010
Spectral problems. Issue dedicated to the memory of M. Birman
Page(s) 317 - 339
DOI https://doi.org/10.1051/mmnp/20105414
Published online 12 May 2010
  1. T. Ando. Comparison of norms |||f(A) − f(B) ||| and |||f(|AB|) |||. Math. Z., 197 (1988), No. 3, 403–409. [CrossRef] [MathSciNet]
  2. N. A. Azamov, A. L. Carey, P. G. Dodds, F. A. Sukochev. Operator integrals, spectral shift, and spectral flow. Canad. J. Math., 61 (2009), No. 2, 241–263. [CrossRef] [MathSciNet]
  3. M. Š.Birman, L. S.Koplienko, M. Z.Solomjak. Estimates of the spectrum of a difference of fractional powers of selfadjoint operators. Izv. Vysš. Učebn. Zaved. Matematika, 154 (1975), No. 3, 3–10.
  4. M. S. Birman, M. Z. Solomyak. Double Stieltjes operator integrals. Problemy Mat. Fiz., (1966), No. 1, 33–67 (Russian).
  5. M. S. Birman, M. Z. Solomyak. Double Stieltjes operator integrals, II. Problemy Mat. Fiz., (1967), No. 2, 26–60 (Russian).
  6. M. S. Birman, M. Z. Solomyak. Double Stieltjes operator integrals, III. Problemy Mat. Fiz., (1973), No. 6, 27–53 (Russian).
  7. Yu. L.Daleckiĭ, S.G. Kreĭn. Formulas of differentiation according to a parameter of functions of Hermitian operators. Doklady Akad. Nauk SSSR (N.S.), 76 (1951), 13–16. [MathSciNet]
  8. Yu. L.Daleckiĭ, S.G. Kreĭn. Integration and differentiation of functions of Hermitian operators and applications to the theory of perturbations. Voronež. Gos. Univ. Trudy Sem. Funkcional. Anal., 1 (1956), 81–105.
  9. A. L.Carey, D. S.Potapov, F. A.Sukochev. Spectral flow is the integral of one forms on Banach manifolds of self adjoint Fredholm operators. Adv. Math, 222 (2009), 1809–1849. [CrossRef] [MathSciNet]
  10. A. Connes, H. Moscovici. Transgression du caractère de Chern et cohomologie cyclique. C. R. Acad. Sci. Paris Sér. I Math., 303 (1986), No. 18, 913–918.
  11. P. G. Dodds, T. K. Dodds. On a submajorization inequality of T. Ando. Operator theory in function spaces and Banach lattices, Oper. Theory Adv. Appl., 75, (1995), 113–131.
  12. P. G. Dodds, F.A. Sukochev. Submajorisation inequalities for convex and concave functions of sums of measurable operators. Positivity, 13 (2009), No. 1, 107–124. [CrossRef] [MathSciNet]
  13. I.C. Gohberg. M.G. Kreĭn. Introduction to the theory of linear nonselfadjoint operators. Translations of Mathematical Monographs, Providence, R.I., AMS, 18, 1969.
  14. N.J. Kalton, F.A Sukochev. Symmetric norms and spaces of operators. J. Reine Angew. Math., 621 (2008), 81–121.
  15. H. Kosaki. Positive definiteness of functions with applications to operator norm inequalities. Preprint, 2009.
  16. B. de Pagter, F. A.Sukochev. Differentiation of operator functions in non-commutative Lp-spaces. J. Funct. Anal., 212 (2004), No. 1, 28–75. [CrossRef] [MathSciNet]
  17. B. de Pagter, F. A. Sukochev. Commutator estimates and R-flows in non-commutative operator spaces. Proc. Edinb. Math. Soc., 50 (2007), No. 2, 293–324. [CrossRef] [MathSciNet]
  18. B. de Pagter, F. A. Sukochev, H. Witvliet. Double operator integrals. J. Funct. Anal., 192 (2002), No. 1, 52–111. [CrossRef] [MathSciNet]
  19. F. Gesztesy, A. Pushnitski, B. Simon. On the Koplienko spectral shift function. I. Basics. Zh. Mat. Fiz. Anal. Geom., 4 (2008), No. 1, 63–107. [MathSciNet]
  20. E. Heinz. Beiträge zur Störungstheorie der Spektralzerlegung. Math. Ann., 123 (1951), 415–438. [CrossRef] [MathSciNet]
  21. A. McIntosh. Heinz inequalities and perturbation of spectral families. Macquarie Mathematical Reports, 79–0006 (1979).
  22. G. Pisier, Q. Xu. Non-commutative Lp-spaces. Handbook of the geometry of Banach spaces, Vol. 2, North-Holland, Amsterdam, 2003, 1459–1517.
  23. D. Potapov, F. Sukochev. Lipschitz and commutator estimates in symmetric operator spaces. J. Operator Theory, 59 (2008), No. 1, 211–234. [MathSciNet]
  24. D. Potapov, F. Sukochev. Unbounded Fredholm modules and double operator integrals. J. Reine Angew. Math., 626 (2009), 159–185. [CrossRef] [MathSciNet]
  25. I.E. Segal. A non-commutative extension of abstract integration. Annals of Mathematics, 57 (1953), 401–457. [CrossRef] [MathSciNet]
  26. B. Simon. Trace ideals and their applications. Mathematical Surveys and Monographs, AMS, Providence, RI, 120 (2005).
  27. F. A. Sukochev, V. I. Chilin. The triangle inequality for operators that are measurable with respect to Hardy-Littlewood order. Izv. Akad. Nauk UzSSR Ser. Fiz.-Mat. Nauk, (1988), No. 4, 44–50 (Russian).
  28. F. A. Sukochev, V. I. Chilin. Symmetric spaces over semifinite von Neumann algebras. Soviet Math. Dokl., 42 (1991), No. 1, 97–101 (Russian). [MathSciNet]
  29. F. A.Sukochev, V. I.Chilin. Weak convergence in non-commutative symmetric spaces. J. Operator Theory, 31 (1994), No. 1, 35–65. [MathSciNet]
  30. J. von Neumann. Some matrix inequalities and metrization of matric-space. Rev. Tomsk Univ., 1 (1937), 286–300.

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.